ABSTRACT
This chapter discusses various operations that can be applied to convert one or more point processes into a new point process. Thinning arises in a variety of circumstances in which points are lost to observation. Translation arises where the points have random velocities, when there is jitter in the recording apparatus, and in a queueing situation where the arrival instant is ‘translated’ into a departure instant. In practice, there may also be a completely random deletion of points because of counter inefficiency. An interesting class of point processes, introduced as a generalization of the Poisson process and defined through the probability generating functional, is the class of Gauss-Poisson processes. The chapter considers some particular examples of dependent deletions which arise in the theory of electronic counters. The counter remains blocked for some interval during which no further particles can be counted.
